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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Unmating of rational maps: Sufficient criteria and examples

Unmating of rational maps: Sufficient criteria and examples

Chapter:
(p.197) Unmating of rational maps: Sufficient criteria and examples
Source:
Frontiers in Complex Dynamics
Author(s):

Daniel Meyer

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0011

This chapter asks when a given (postcritically finite) rational map f arises as a mating. Mating occurs when the filled Julia sets of two polynomials of the same degree are dynamically related via external rays. This chapter seeks to tackle the opposite of mating—nonmating. To do this, a sufficient condition when the given rational map f arises as a mating is given. If this condition is satisfied, the chapter presents a simple explicit algorithm to unmate the rational map. This means that f is decomposed into polynomials that, when mated, yield f. Several examples of unmatings are then presented.

Keywords:   mating, unmating, rational maps, external rays, decomposition, polynomials

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